A new admissibility condition for descriptor delay systems
Based on Lyapunov's second method and limited equivalent transformations of descriptor systems,combined with the integral inequality technique,an admissibility condition for descriptor delay systems is given in the form of linear matrix inequality(LMI).Firstly,it is concluded that the descriptor delay system is regular and impulse free by using limited equivalent transformations of descriptor systems.Secondly,a new Lyapunov-Krasovskii functional(L-K functional)is constructed by selecting the augmented L-K functional,multiple integral L-K functional and introducting the relaxed L-K functional,and then,the integral terms producted by derivation of L-K functional are dealt with by Jensen integral inequality and Wirtinger integral inequality,respectively.Thus,a stability condition for the descriptor delay system is obtained,correspondingly,an admissibility condition for the descriptor delay system is obtained.Finally,a numerical example is provided to demonstrate feasibility and validity of the proposed method by virtue of LMI toolbox of MATLAB.
descriptor delay systemsadmissibility conditionLyapunov-Krasovskii functionalJensen integral inequalityWirtinger integral inequality
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